Optical constants

Refractive index of BAK4 (HIKARI)

BAK4: n,k 0.4–0.7 µm

Data: formula 3 + tabulated k
Range: 0.4–0.7 µm
Temperature: 293 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.56883
Extinction coefficient k: 1.76522e-08

Permittivity ε₁: 2.46122
Permittivity ε₂: 5.53866e-08

Absorption coefficient α: 0.00377509 cm⁻¹
Penetration depth δ = λ/(2πk): 5.29788e+09 nm

Abbe number V_d: 56.049
Chromatic dispersion dn/dλ: -0.0524403 µm⁻¹

Group index n_g: 1.59964
Group velocity dispersion: 93.0086 fs²/mm

Dispersion parameter D: -507.411 ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.

Use it in Lightsmith

Load this data in Python, simulate in one more line

pip install lightsmith

import lightsmith as ls

# BAK4 (HIKARI): BAK4
hikari_bak4 = ls.fetch_refractiveindex("specs", "HIKARI-optical", "BAK4", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hikari_bak4.range_nm)  # (400, 700) nm
eps = hikari_bak4.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_76caa49f982d/lightsmith"
hikari_bak4 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(hikari_bak4.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (hikari-bak4/hikari).

# ... load hikari_bak4 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=hikari_bak4)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=700, num=81),
)
res = ls.solve(sim)  # exact Mie for a sphere
print(res.q_ext)     # extinction efficiency at each wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.

Dispersion formula

Polynomial (formula 3), λ in µm

n^{2} = 2.414299 - 0.002829974 λ^{2.0} + 0.01680892 λ^{- 2.0} - 8.945119 \times 10^{-5} λ^{- 4.0} - 1.350522 \times 10^{-5} λ^{- 6.0} + 4.145336 \times 10^{-6} λ^{- 8.0}

Valid from 0.4 to 0.7 µm.

Coefficients as stored

C_i	Value
C1	2.414299
C2	-0.002829974
C3	2.0
C4	0.01680892
C5	-2.0
C6	-8.945119e-05
C7	-4.0
C8	-1.350522e-05
C9	-6.0
C10	4.145336e-06
C11	-8.0

Comments and conditions

Conditions

temperature: 293 K

Properties

nd: 1.568829
Vd: 56.049408
glass code: 569560
glass status: preferred
density: value: 3100
thermal expansion: value: 8.3e-06, temperature range: 243 343
dPgF: -0.0033

References

NIKON Zemax catalog 2017-11 (obtained from http://www.nikon.com)
See also HIKARI glass data sheets

Cite

NIKON Zemax catalog 2017-11 (obtained from http://www.nikon.com); See also HIKARI glass data sheets; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 408 wavelengths, the same grid as the API and the library

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

BAK4 (HIKARI), BAK4: n and k versus wavelength
λ (µm)	n	k
0.4	1.586958	2.877800e-08
0.400561	1.586858	2.881837e-08
0.401124	1.586757	2.885879e-08
0.401687	1.586658	2.889927e-08
0.40225	1.586558	2.893980e-08
0.402815	1.586459	2.898039e-08
0.40338	1.586361	2.902104e-08
0.403946	1.586263	2.906175e-08
0.404513	1.586165	2.910251e-08
0.405081	1.586068	2.914334e-08
0.40565	1.58597	2.918421e-08
0.406219	1.585874	2.922515e-08
0.406789	1.585778	2.926614e-08
0.40736	1.585682	2.930719e-08
0.407932	1.585586	2.934830e-08
0.408504	1.585491	2.938947e-08
0.409078	1.585396	2.943069e-08
0.409652	1.585301	2.947197e-08
0.410227	1.585207	2.951331e-08
0.410803	1.585113	2.955471e-08
0.411379	1.58502	2.959617e-08
0.411957	1.584927	2.963768e-08
0.412535	1.584834	2.967925e-08
0.413114	1.584742	2.972088e-08
0.413694	1.58465	2.976257e-08
0.414274	1.584558	2.980432e-08
0.414856	1.584467	2.984612e-08
0.415438	1.584375	2.988799e-08
0.416021	1.584285	2.992991e-08
0.416605	1.584194	2.997189e-08
0.41719	1.584104	3.001394e-08
0.417775	1.584014	3.005604e-08
0.418362	1.583925	3.009820e-08
0.418949	1.583836	3.014041e-08
0.419537	1.583747	3.018269e-08
0.42	1.583678	3.021600e-08
0.420126	1.583659	3.024723e-08
0.420715	1.583571	3.039388e-08
0.421306	1.583483	3.054073e-08
0.421897	1.583395	3.068779e-08
0.422489	1.583308	3.083506e-08
0.423082	1.583221	3.098253e-08
0.423676	1.583135	3.113021e-08
0.424271	1.583048	3.127810e-08
0.424866	1.582962	3.142619e-08
0.425462	1.582877	3.157450e-08
0.42606	1.582791	3.172301e-08
0.426658	1.582706	3.187173e-08
0.427256	1.582621	3.202066e-08
0.427856	1.582537	3.216979e-08
0.428457	1.582453	3.231914e-08
0.429058	1.582369	3.246870e-08
0.42966	1.582285	3.261846e-08
0.430263	1.582202	3.276844e-08
0.430867	1.582119	3.291862e-08
0.431472	1.582036	3.306902e-08
0.432077	1.581954	3.321963e-08
0.432684	1.581871	3.337045e-08
0.433291	1.58179	3.352148e-08
0.433899	1.581708	3.367273e-08
0.434508	1.581627	3.382418e-08
0.435118	1.581545	3.397585e-08
0.435729	1.581465	3.412773e-08
0.43634	1.581384	3.427983e-08
0.436953	1.581304	3.443213e-08
0.437566	1.581224	3.458466e-08
0.43818	1.581144	3.473739e-08
0.438795	1.581065	3.489034e-08
0.439411	1.580986	3.504351e-08
0.44	1.58091	3.519000e-08
0.440028	1.580907	3.519222e-08
0.440645	1.580828	3.524162e-08
0.441264	1.58075	3.529110e-08
0.441883	1.580671	3.534065e-08
0.442503	1.580594	3.539026e-08
0.443124	1.580516	3.543995e-08
0.443746	1.580439	3.548970e-08
0.444369	1.580362	3.553953e-08
0.444993	1.580285	3.558942e-08
0.445617	1.580208	3.563939e-08
0.446243	1.580132	3.568942e-08
0.446869	1.580056	3.573953e-08
0.447496	1.57998	3.578970e-08
0.448124	1.579904	3.583995e-08
0.448753	1.579829	3.589026e-08
0.449383	1.579754	3.594065e-08
0.450014	1.579679	3.599111e-08
0.450645	1.579604	3.604164e-08
0.451278	1.57953	3.609224e-08
0.451911	1.579456	3.614291e-08
0.452546	1.579382	3.619365e-08
0.453181	1.579308	3.624446e-08
0.453817	1.579235	3.629535e-08
0.454454	1.579161	3.634630e-08
0.455092	1.579088	3.639733e-08
0.45573	1.579016	3.644843e-08
0.45637	1.578943	3.649960e-08
0.457011	1.578871	3.655084e-08
0.457652	1.578799	3.660216e-08
0.458294	1.578727	3.665354e-08
0.458938	1.578655	3.670500e-08
0.459582	1.578584	3.675653e-08
0.46	1.578538	3.679000e-08
0.460227	1.578513	3.667714e-08
0.460873	1.578442	3.635553e-08
0.461519	1.578371	3.603346e-08
0.462167	1.578301	3.571094e-08
0.462816	1.578231	3.538797e-08
0.463465	1.578161	3.506455e-08
0.464116	1.578091	3.474067e-08
0.464767	1.578021	3.441634e-08
0.46542	1.577952	3.409155e-08
0.466073	1.577883	3.376631e-08
0.466727	1.577814	3.344061e-08
0.467382	1.577745	3.311445e-08
0.468038	1.577676	3.278784e-08
0.468695	1.577608	3.246076e-08
0.469353	1.57754	3.213323e-08
0.470012	1.577472	3.180524e-08
0.470671	1.577404	3.147679e-08
0.471332	1.577337	3.114787e-08
0.471993	1.57727	3.081850e-08
0.472656	1.577202	3.048866e-08
0.473319	1.577136	3.015836e-08
0.473984	1.577069	2.982760e-08
0.474649	1.577002	2.949637e-08
0.475315	1.576936	2.916468e-08
0.475982	1.57687	2.883252e-08
0.47665	1.576804	2.849989e-08
0.477319	1.576739	2.816680e-08
0.477989	1.576673	2.783324e-08
0.47866	1.576608	2.749921e-08
0.479332	1.576543	2.716472e-08
0.48	1.576478	2.683200e-08
0.480005	1.576478	2.683135e-08
0.480678	1.576413	2.673410e-08
0.481353	1.576349	2.663671e-08
0.482028	1.576285	2.653919e-08
0.482705	1.57622	2.644153e-08
0.483382	1.576157	2.634374e-08
0.484061	1.576093	2.624581e-08
0.48474	1.576029	2.614773e-08
0.485421	1.575966	2.604953e-08
0.486102	1.575903	2.595118e-08
0.486784	1.57584	2.585270e-08
0.487467	1.575777	2.575407e-08
0.488152	1.575714	2.565531e-08
0.488837	1.575652	2.555641e-08
0.489523	1.57559	2.545738e-08
0.49021	1.575528	2.535820e-08
0.490898	1.575466	2.525888e-08
0.491587	1.575404	2.515943e-08
0.492277	1.575343	2.505983e-08
0.492968	1.575281	2.496010e-08
0.49366	1.57522	2.486022e-08
0.494353	1.575159	2.476021e-08
0.495046	1.575099	2.466005e-08
0.495741	1.575038	2.455975e-08
0.496437	1.574978	2.445932e-08
0.497134	1.574917	2.435874e-08
0.497832	1.574857	2.425802e-08
0.49853	1.574797	2.415716e-08
0.49923	1.574738	2.405616e-08
0.499931	1.574678	2.395501e-08
0.5	1.574672	2.394500e-08
0.500632	1.574619	2.380849e-08
0.501335	1.57456	2.365679e-08
0.502039	1.574501	2.350487e-08
0.502743	1.574442	2.335274e-08
0.503449	1.574383	2.320040e-08
0.504155	1.574325	2.304784e-08
0.504863	1.574266	2.289507e-08
0.505572	1.574208	2.274209e-08
0.506281	1.57415	2.258889e-08
0.506992	1.574092	2.243547e-08
0.507703	1.574034	2.228184e-08
0.508416	1.573977	2.212800e-08
0.50913	1.57392	2.197394e-08
0.509844	1.573862	2.181966e-08
0.51056	1.573805	2.166517e-08
0.511276	1.573749	2.151046e-08
0.511994	1.573692	2.135553e-08
0.512712	1.573635	2.120038e-08
0.513432	1.573579	2.104502e-08
0.514153	1.573523	2.088944e-08
0.514874	1.573467	2.073364e-08
0.515597	1.573411	2.057762e-08
0.516321	1.573355	2.042138e-08
0.517045	1.573299	2.026493e-08
0.517771	1.573244	2.010825e-08
0.518498	1.573189	1.995135e-08
0.519225	1.573134	1.979424e-08
0.519954	1.573079	1.963690e-08
0.520684	1.573024	1.947934e-08
0.521415	1.572969	1.932156e-08
0.522147	1.572915	1.916356e-08
0.522879	1.57286	1.900534e-08
0.523613	1.572806	1.884690e-08
0.524348	1.572752	1.868823e-08
0.525084	1.572698	1.852934e-08
0.525821	1.572645	1.837023e-08
0.526559	1.572591	1.821090e-08
0.527298	1.572538	1.805134e-08
0.528038	1.572484	1.789155e-08
0.528779	1.572431	1.773155e-08
0.529521	1.572378	1.757131e-08
0.530265	1.572325	1.741086e-08
0.531009	1.572273	1.725018e-08
0.531754	1.57222	1.708927e-08
0.532501	1.572168	1.692814e-08
0.533248	1.572116	1.676678e-08
0.533996	1.572063	1.660519e-08
0.534746	1.572012	1.644338e-08
0.535496	1.57196	1.628134e-08
0.536248	1.571908	1.611907e-08
0.537001	1.571857	1.595658e-08
0.537754	1.571805	1.579385e-08
0.538509	1.571754	1.563090e-08
0.539265	1.571703	1.546772e-08
0.540022	1.571652	1.530431e-08
0.54078	1.571601	1.514067e-08
0.541539	1.57155	1.497680e-08
0.542299	1.5715	1.481271e-08
0.54306	1.571449	1.464838e-08
0.543822	1.571399	1.448382e-08
0.544585	1.571349	1.431903e-08
0.54535	1.571299	1.415401e-08
0.546115	1.571249	1.398875e-08
0.546882	1.5712	1.382327e-08
0.547649	1.57115	1.365755e-08
0.548418	1.571101	1.349160e-08
0.549187	1.571051	1.332542e-08
0.549958	1.571002	1.315900e-08
0.55	1.570999	1.315000e-08
0.55073	1.570953	1.323743e-08
0.551503	1.570904	1.332999e-08
0.552277	1.570855	1.342267e-08
0.553052	1.570807	1.351549e-08
0.553829	1.570758	1.360843e-08
0.554606	1.57071	1.370151e-08
0.555384	1.570662	1.379471e-08
0.556164	1.570614	1.388805e-08
0.556944	1.570566	1.398152e-08
0.557726	1.570518	1.407512e-08
0.558509	1.57047	1.416885e-08
0.559293	1.570423	1.426271e-08
0.560078	1.570375	1.435671e-08
0.560864	1.570328	1.445083e-08
0.561651	1.570281	1.454509e-08
0.562439	1.570233	1.463948e-08
0.563229	1.570187	1.473400e-08
0.564019	1.57014	1.482866e-08
0.564811	1.570093	1.492345e-08
0.565604	1.570046	1.501837e-08
0.566397	1.57	1.511342e-08
0.567192	1.569954	1.520861e-08
0.567988	1.569908	1.530393e-08
0.568786	1.569862	1.539939e-08
0.569584	1.569816	1.549498e-08
0.570383	1.56977	1.559070e-08
0.571184	1.569724	1.568656e-08
0.571986	1.569679	1.578255e-08
0.572788	1.569633	1.587868e-08
0.573592	1.569588	1.597494e-08
0.574397	1.569543	1.607134e-08
0.575204	1.569498	1.616787e-08
0.576011	1.569453	1.626454e-08
0.576819	1.569408	1.636134e-08
0.577629	1.569363	1.645828e-08
0.57844	1.569318	1.655536e-08
0.579251	1.569274	1.665257e-08
0.580064	1.56923	1.674992e-08
0.580879	1.569185	1.684740e-08
0.581694	1.569141	1.694502e-08
0.58251	1.569097	1.704278e-08
0.583328	1.569053	1.714068e-08
0.584147	1.56901	1.723871e-08
0.584966	1.568966	1.733688e-08
0.585787	1.568922	1.743519e-08
0.58661	1.568879	1.753364e-08
0.587433	1.568836	1.763222e-08
0.588257	1.568793	1.773094e-08
0.589083	1.568749	1.782981e-08
0.58991	1.568707	1.792881e-08
0.590738	1.568664	1.802795e-08
0.591567	1.568621	1.812722e-08
0.592397	1.568578	1.822664e-08
0.593229	1.568536	1.832620e-08
0.594061	1.568493	1.842590e-08
0.594895	1.568451	1.852573e-08
0.59573	1.568409	1.862571e-08
0.596566	1.568367	1.872583e-08
0.597403	1.568325	1.882609e-08
0.598242	1.568283	1.892649e-08
0.599082	1.568241	1.902703e-08
0.599922	1.5682	1.912771e-08
0.6	1.568196	1.913700e-08
0.600764	1.568158	1.908202e-08
0.601608	1.568117	1.902138e-08
0.602452	1.568076	1.896065e-08
0.603298	1.568035	1.889984e-08
0.604144	1.567993	1.883894e-08
0.604992	1.567953	1.877796e-08
0.605841	1.567912	1.871689e-08
0.606692	1.567871	1.865574e-08
0.607543	1.56783	1.859450e-08
0.608396	1.56779	1.853317e-08
0.60925	1.567749	1.847176e-08
0.610105	1.567709	1.841026e-08
0.610961	1.567669	1.834867e-08
0.611819	1.567629	1.828700e-08
0.612677	1.567589	1.822524e-08
0.613537	1.567549	1.816340e-08
0.614398	1.567509	1.810147e-08
0.615261	1.567469	1.803945e-08
0.616124	1.56743	1.797734e-08
0.616989	1.56739	1.791515e-08
0.617855	1.567351	1.785287e-08
0.618722	1.567312	1.779050e-08
0.619591	1.567273	1.772805e-08
0.62046	1.567233	1.766551e-08
0.621331	1.567195	1.760288e-08
0.622203	1.567156	1.754016e-08
0.623076	1.567117	1.747735e-08
0.623951	1.567078	1.741446e-08
0.624827	1.56704	1.735147e-08
0.625704	1.567001	1.728840e-08
0.626582	1.566963	1.722524e-08
0.627461	1.566925	1.716199e-08
0.628342	1.566887	1.709866e-08
0.629224	1.566848	1.703523e-08
0.630107	1.56681	1.697172e-08
0.630991	1.566773	1.690811e-08
0.631877	1.566735	1.684442e-08
0.632764	1.566697	1.678064e-08
0.633652	1.56666	1.671676e-08
0.634541	1.566622	1.665280e-08
0.635432	1.566585	1.658875e-08
0.636324	1.566548	1.652461e-08
0.637217	1.56651	1.646038e-08
0.638111	1.566473	1.639605e-08
0.639007	1.566436	1.633164e-08
0.639904	1.566399	1.626714e-08
0.640802	1.566363	1.620255e-08
0.641701	1.566326	1.613786e-08
0.642602	1.566289	1.607309e-08
0.643504	1.566253	1.600822e-08
0.644407	1.566216	1.594327e-08
0.645311	1.56618	1.587822e-08
0.646217	1.566144	1.581308e-08
0.647124	1.566108	1.574785e-08
0.648032	1.566072	1.568253e-08
0.648942	1.566036	1.561711e-08
0.649852	1.566	1.555161e-08
0.65	1.565994	1.554100e-08
0.650765	1.565964	1.538858e-08
0.651678	1.565929	1.520649e-08
0.652593	1.565893	1.502415e-08
0.653509	1.565857	1.484155e-08
0.654426	1.565822	1.465870e-08
0.655344	1.565787	1.447559e-08
0.656264	1.565752	1.429222e-08
0.657185	1.565716	1.410860e-08
0.658108	1.565681	1.392472e-08
0.659031	1.565646	1.374058e-08
0.659956	1.565612	1.355618e-08
0.660882	1.565577	1.337152e-08
0.66181	1.565542	1.318661e-08
0.662739	1.565508	1.300143e-08
0.663669	1.565473	1.281599e-08
0.664601	1.565439	1.263030e-08
0.665533	1.565404	1.244434e-08
0.666467	1.56537	1.225812e-08
0.667403	1.565336	1.207165e-08
0.66834	1.565302	1.188490e-08
0.669278	1.565268	1.169790e-08
0.670217	1.565234	1.151064e-08
0.671158	1.5652	1.132311e-08
0.6721	1.565167	1.113532e-08
0.673043	1.565133	1.094726e-08
0.673988	1.565099	1.075894e-08
0.674933	1.565066	1.057036e-08
0.675881	1.565033	1.038151e-08
0.676829	1.564999	1.019240e-08
0.677779	1.564966	1.000302e-08
0.678731	1.564933	9.813377e-09
0.679683	1.5649	9.623467e-09
0.680637	1.564867	9.433290e-09
0.681592	1.564834	9.242847e-09
0.682549	1.564801	9.052136e-09
0.683507	1.564769	8.861157e-09
0.684466	1.564736	8.669910e-09
0.685427	1.564704	8.478395e-09
0.686389	1.564671	8.286611e-09
0.687352	1.564639	8.094558e-09
0.688317	1.564606	7.902235e-09
0.689283	1.564574	7.709643e-09
0.690251	1.564542	7.516780e-09
0.691219	1.56451	7.323646e-09
0.69219	1.564478	7.130242e-09
0.693161	1.564446	6.936565e-09
0.694134	1.564414	6.742618e-09
0.695108	1.564383	6.548397e-09
0.696084	1.564351	6.353905e-09
0.697061	1.56432	6.159139e-09
0.698039	1.564288	5.964100e-09
0.699019	1.564257	5.768787e-09
0.7	1.564225	5.573200e-09

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

BAK4 (HIKARI): all datasets

BaK (Barium crown)

BAK4 n,k 0.4–0.7 µm default

About BAK4 (HIKARI)

Hikari Glass Co., Ltd. is a Japanese company specializing in the manufacturing of high-quality optical glass and optical components, and is a subsidiary of Nikon Corporation. Known for its precision engineering and strict quality control, Hikari serves various industries including consumer electronics, scientific research, and industrial optics. The company offers a wide range of specialized optical materials, including various types of crown and flint glasses, which are used in applications demanding high levels of optical clarity and performance. Hikari's products often find use in lenses, prisms, and other optical elements where precision and reliability are critical. With the backing of Nikon's renowned expertise in optics and imaging, Hikari has become a respected name in the field of optics, serving both domestic and international markets. Their expertise in crafting custom solutions for complex optical requirements has made them a preferred choice for organizations in need of specialized glass materials. As a testament to their commitment to quality, Hikari Glass Co., Ltd. is often sought after for projects requiring the highest levels of optical performance and integrity.

More about BAK4 (HIKARI) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/specs/hikari/optical/BAK4.yml
ID: ds_76caa49f982d
API: /v1/datasets/ds_76caa49f982d

Plot